Did dinosaurs and man coexist?

Taxonomy is being changed by the adoption of Cladistics. Under Cladism groups include all the descendants of that group - so, granting that birds are descended from dinosaurs, birds would be considered dinosaurs.

That would depend on the way the groups are drawn. The ancestors of mammals are classified as synapsids, rather than reptiles.Introduction to the Synapsida
"These pre-mammalian groups of synapsids have at times been called "mammal-like reptiles". This term is now discouraged because although many had characteristics in common with mammals, none of them were actually reptiles"However, "fish" seems to be a term used for the "basal vertebrates" (same site) so, on that basis humans could be classified as fish .This site is also worth a look: Tree of Life Web Project